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728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Results for “error correction” 17 papers
Ultrametric. Non-Archimedean geometry: tree metrics, strong triangle inequality, hierarchical distance Tagged papers: 115.
Ultrametric Tree Encoding for Passive Quantum Error Confinement: Support Confinement, Barrier Models, and the Limits of the Strong Triangle Inequality
Scalable quantum computing is blocked by the overhead of active error correction: surface-code implementations require on the order of $10^{3}$ physical qubits per logical qubit, repeated syndrome extraction, and low-latency decoding. A recent proposal claims that encoding logical information on a…
Error Confinement Theorem for Ultrametric Decoders and Its Implications for Quantum Error Correction
Fault‑tolerant quantum computing is impeded by the large qubit overhead required for active quantum error correction (QEC). Existing decoders either lack rigorous hierarchical guarantees or incur computational costs that scale with the full syndrome volume. We model a symmetric decoder with $p\ge 3$…
Passive Quantum Error Correction via Ultrametric Geometry on Bruhat–Tits Trees
Scalable quantum computing is limited by the thermodynamic overhead of active error‑correction cycles, which require repeated syndrome extraction, low‑latency decoding, and large ancilla resources. A quantitative gap exists: no fully derived account shows how non‑Archimedean (ultrametric) geometry…
Ultrametric Passive Fault Tolerance on Bruhat–Tits Trees: Analytic Derivation and Quantitative Projections
Quantum computing today is limited by the large physical‑to‑logical qubit overhead required for active error correction, which demands frequent syndrome extraction, low‑latency decoding, and extensive ancilla resources. A proposed alternative encodes logical information on the vertices of a $p$‑adic…
p‑Adic Lift‑and‑Shift: Transplanting Elementary Calculus to the 2‑adic Tree and a Primary‑Education Blueprint
Elementary analysis is taught exclusively on the Archimedean real line, yet many scientific domains—hierarchical data mining, ultrametric phylogenetics, and quantum error correction—operate naturally on non‑Archimedean structures. This paper closes the gap by (i) formally identifying the points at…
Ultrametric Passive Fault Tolerance on Bruhat–Tits Trees: Analytic Derivation and Numerical Projections
Fault‑tolerant quantum computation currently demands a physical‑to‑logical qubit overhead of $10^{2}$–$10^{4}$, a cost that limits near‑term scalability. A major gap is the lack of a passive protection mechanism that does not require syndrome extraction or additional ancilla qubits. We analytically…
Regular Ternary Tree Codes and Symmetric Exponential Energy Barriers for Passive Quantum Error Correction
Quantum error correction (QEC) currently relies on active syndrome extraction, which incurs large qubit overheads. A conjectured passive scheme encodes logical information on the vertices of a regular ternary Bruhat–Tits tree, exploiting the ultrametric triangle inequality to create an energy…
Ultrametric Passive Error Correction on \(p\)-ary Bruhat–Tits Trees: Barrier Analysis and Recursive Thresholds
Fault‑tolerant quantum computation presently depends on active stabilizer codes such as the surface code, which require repeated syndrome extraction, low‑latency decoding, and large ancilla overhead. A fundamentally different approach would encode logical qubits on the vertices of a regular…
Ultrametric Quantum Error Correction on Bruhat–Tits Trees: Energy Barriers, Classical Evidence, and the Quantization Question
Passive fault tolerance—protection of logical qubits by encoding geometry alone, without repeated syndrome measurement—would remove the dominant overhead in scalable quantum computing if it could be made to work for quantum information rather than only for classical bits. We study a conjectured…
Ultrametric Geometry as Passive Quantum Error Correction: Bruhat–Tits Qudit Codes and the Non-Archimedean Bound
Active quantum error correction (QEC) dominates the overhead of scalable quantum processors, requiring repeated syndrome extraction, low-latency decoding, and large ancilla counts that inflate hardware cost and energy consumption. A passive alternative that eliminates measurement cycles would reduce…
Archimedean Shadows: The QEC-Darwinism Tradeoff in Ultrametric Spaces
Maity et al. (arXiv:2608.03944, 2026) proved that quantum error correction and Quantum Darwinism cannot coexist above a critical logical fidelity $F_L > 0.874$ — a tight, model-independent no-go theorem establishing an exact tradeoff between protected quantum information and emergent classical…
Passive Error Resilience Through Ultrametric Geometry: A Proposal for p-Adic Quantum Metrology
Active quantum error correction is the dominant paradigm for achieving fault-tolerant quantum computation, but its thermodynamic cost at utility scale remains unaddressed. Each round of syndrome extraction, decoding, and feedback erases information — and under Landauer's principle, that erasure…
Ultrametric Consilience Atlas: Cross-Domain Applications of p-Adic Mathematical Structure
A single mathematical structure — the p-adic ultrametric topology — appears in apparently unrelated domains: quantum error correction (stabilizer codes), protein folding (energy landscapes), neural coding (population activity clustering), financial markets (hierarchical correlation), climate…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection for Majorana Qubits
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Computational Simulation of Geometric Orientation Codes
Fault-tolerant quantum computing requires robust error correction traditionally met using planar topologies that assume noise is perfectly isotropic. However, recent astrophysical measurements suggest the universe possesses fundamental anisotropic properties. This paper challenges the isotropic…
Ultrametric Relaxation Dynamics in Topological Quantum Memory
The scalability of Topological Quantum Computing (TQC) is currently impeded by a “Thermodynamic Wall,” where the entropy generation from active error correction cycles scales exponentially with logical qubit count. This paper proposes a paradigm shift from active gate synthesis to passive…
Qudit Quantum Error Correction
The observation that positional notation carries a native ultrametric tree structure extends into quantum computing through the tensor-product architecture of qubit registers. We formalize three theses: (I) a tree-topology quantum processor confines errors to subtrees via the strong triangle…
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